Fourier-Mukai partners for very general special cubic fourfolds

We exhibit explicit examples of very general special cubic fourfolds with discriminant d admitting an associated (twisted) K3 surface, which have non-isomorphic Fourier-Mukai partners. In particular, in the untwisted setting, we show that the number of Fourier-Mukai partners for a very general special cubic fourfold with discriminant d and having an associated K3 surface, is equal to the number m of Fourier-Mukai partners of its associated K3 surface, if d equivalent to 2(mod 6); else, if d equivalent to 0(mod 6), the cubic fourfold has inverted right perpendicularm/2inverted left perpendicular Fourier-Mukai partners.